Disclosed herein is a method for generating a composite cryptographic signature. The method comprises receiving a message and a first part of a first party signature, wherein the first part of the first party signature is derived from the message and a first share of a first private key. The method further comprises generating a first party signature from the first part of the first party signature and a second share of the first private key and generating a second party signature from the message and a second private key. The method further comprises combining the first party signature and the second party signature to generate a composite cryptographic signature. An apparatus, a computer-readable medium for implementing this method are also disclosed.